Internal problem ID [5312]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary
problems. Page 39
Problem number: 19 (q).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {y^{2}-\left (x y+2 y+y^{3}\right ) y^{\prime }=-2} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve((2+y(x)^2)-(x*y(x)+2*y(x)+y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
\[ x -y \left (x \right )^{2}-2-\sqrt {y \left (x \right )^{2}+2}\, c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 5.808 (sec). Leaf size: 189
DSolve[(2+y[x]^2)-(x*y[x]+2*y[x]+y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {2 x-\sqrt {4 c_1{}^2 x+c_1{}^4}-4+c_1{}^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {2 x-\sqrt {4 c_1{}^2 x+c_1{}^4}-4+c_1{}^2}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {2 x+\sqrt {4 c_1{}^2 x+c_1{}^4}-4+c_1{}^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {2 x+\sqrt {4 c_1{}^2 x+c_1{}^4}-4+c_1{}^2}}{\sqrt {2}} \\ y(x)\to -i \sqrt {2} \\ y(x)\to i \sqrt {2} \\ \end{align*}